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Topological r-Entropy of Symbolic Dynamical System

Ren Yunli, Jinfeng Lv, HE Shang-qin

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Abstract

Topological r-entropy is a newly defined entropy which weakens the requirement of Bowen's spanning set. In this paper, an upper bound of topological r-entropy of symbolic dynamical system is acquired, which illustrates that the strict inequality between topological r-entropy and topological entropy may hold for some systems. Meanwhile, we acquire a relation among measure-theoretic r-entropies with different deltas.

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What this paper is about

Topological r-entropy is a newly defined entropy which weakens the requirement of Bowen's spanning set. In this paper, an upper bound of topological r-entropy of symbolic dynamical system is acquired, which illustrates that the strict inequality between topological r-entropy and topological entropy may hold for some systems. Meanwhile, we acquire a relation among measure-theoretic r-entropies with different deltas.

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Available abstract

Topological r-entropy is a newly defined entropy which weakens the requirement of Bowen's spanning set. In this paper, an upper bound of topological r-entropy of symbolic dynamical system is acquired, which illustrates that the strict inequality between topological r-entropy and topological entropy may hold for some systems. Meanwhile, we acquire a relation among measure-theoretic r-entropies with different deltas.

Key concepts: Topological entropy, Topological entropy in physics, Entropy (arrow of time), Mathematics, Topology (electrical circuits), Maximum entropy probability distribution, Dynamical systems theory, Joint quantum entropy

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